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Paul Matthieu Hermann Laurent
Paul Matthieu Hermann Laurent (2 September 1841, in Luxembourg City – 19 February 1908, in Paris, France) was a French mathematician. Despite his large body of works, Laurent series expansions for complex functions were ''not'' named after him, but after Pierre Alphonse Laurent. Publications * * * * * * References External links * * * (not born in Echternach Echternach ( lb, Iechternach or (locally) ) is a commune with town status in the canton of Echternach, which is part of the district of Grevenmacher, in eastern Luxembourg. Echternach lies near the border with Germany, and is the oldest town in ...) 1841 births 1908 deaths People from Echternach 19th-century French mathematicians 20th-century French mathematicians Mathematical analysts {{France-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luxembourg City
Luxembourg ( lb, Lëtzebuerg; french: Luxembourg; german: Luxemburg), also known as Luxembourg City ( lb, Stad Lëtzebuerg, link=no or ; french: Ville de Luxembourg, link=no; german: Stadt Luxemburg, link=no or ), is the capital city of the Grand Duchy of Luxembourg and the country's most populous commune. Standing at the confluence of the Alzette and Pétrusse rivers in southern Luxembourg, the city lies at the heart of Western Europe, situated by road from Brussels, from Paris, and from Cologne. The city contains Luxembourg Castle, established by the Franks in the Early Middle Ages, around which a settlement developed. , Luxembourg City has a population of 128,514 inhabitants, which is more than three times the population of the country's second most populous commune ( Esch-sur-Alzette). The city's population consists of 160 nationalities. Foreigners represent 70% of the city's population, whilst Luxembourgers represent 30% of the population; the number of foreign-bor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paris
Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, fashion, gastronomy, and science. For its leading role in the arts and sciences, as well as its very early system of street lighting, in the 19th century it became known as "the City of Light". Like London, prior to the Second World War, it was also sometimes called the capital of the world. The City of Paris is the centre of the Île-de-France region, or Paris Region, with an estimated population of 12,262,544 in 2019, or about 19% of the population of France, making the region France's primate city. The Paris Region had a GDP of €739 billion ($743 billion) in 2019, which is the highest in Europe. According to the Economis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans. Its metropolitan area extends from the Rhine to the Atlantic Ocean and from the Mediterranean Sea to the English Channel and the North Sea; overseas territories include French Guiana in South America, Saint Pierre and Miquelon in the North Atlantic, the French West Indies, and many islands in Oceania and the Indian Ocean. Due to its several coastal territories, France has the largest exclusive economic zone in the world. France borders Belgium, Luxembourg, Germany, Switzerland, Monaco, Italy, Andorra, and Spain in continental Europe, as well as the Netherlands, Suriname, and Brazil in the Americas via its overseas territories in French Guiana and Saint Martin. Its eighteen integral regions (five of which are overseas) span a combined area of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laurent Series
In mathematics, the Laurent series of a complex function f(z) is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be applied. The Laurent series was named after and first published by Pierre Alphonse Laurent in 1843. Karl Weierstrass may have discovered it first in a paper written in 1841, but it was not published until after his death.. Definition The Laurent series for a complex function f(z) about a point c is given by f(z) = \sum_^\infty a_n(z-c)^n, where a_n and c are constants, with a_n defined by a line integral that generalizes Cauchy's integral formula: a_n =\frac\oint_\gamma \frac \, dz. The path of integration \gamma is counterclockwise around a Jordan curve enclosing c and lying in an annulus A in which f(z) is holomorphic (analytic). The expansion for f(z) will then be valid anywhere inside the annulus. The annulus is shown in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Function
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to its Taylor series (that is, it is analytic), complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions). History Complex analysis is one of the classical branches in mathematics, with roots in the 18th century and just prior. Important mathematicians associated with complex num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Alphonse Laurent
Pierre Alphonse Laurent (18 July 1813 – 2 September 1854) was a French mathematician, engineer, and Military Officer best known for discovering the Laurent series, an expansion of a function into an infinite power series, generalizing the Taylor series expansion. He was born in Paris, France. His father, Pierre Michel Laurent (1769 – 1841) was French, whereas his mother, Eleanor Cheshire (1778 – 1840) was English. Pierre Laurent entered the École Polytechnique in Paris in 1830 and graduated in 1832 as one of the best students in his year. Afterwards, he joined the engineering corps as a second lieutenant, before attending the École d'Application at Metz until he was sent to Algeria. Laurent returned to France from Algeria around 1840 and spent six years directing operations for the enlargement of the port of Le Havre on the English Channel coast. Rouen had been the main French port up to the nineteenth century but the hydraulic construction projects on which Laurent wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Echternach
Echternach ( lb, Iechternach or (locally) ) is a commune with town status in the canton of Echternach, which is part of the district of Grevenmacher, in eastern Luxembourg. Echternach lies near the border with Germany, and is the oldest town in Luxembourg. History The town grew around the Abbey of Echternach, which was founded in 698 by St Willibrord, an English monk from Ripon, Northumbria (in present-day North Yorkshire, England), who became the first bishop of Utrecht and worked to Christianize the Frisians. As bishop, he was the Echternach monastery's abbot until his death in 739. It is in his honour that the notable Dancing procession of Echternach takes place annually on Whit Tuesday. The river Sauer that flows past the town now forms the border between Luxembourg and Germany; in the later Roman Empire and under the Merovingians by contrast, the Sauer did not form a border or march in this area. The Roman villa at Echternach (traces of which were rediscovered ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1841 Births
Events January–March * January 20 – Charles Elliot of the United Kingdom, and Qishan of the Qing dynasty, agree to the Convention of Chuenpi. * January 26 – Britain occupies Hong Kong. Later in the year, the first census of the island records a population of about 7,500. * January 27 – The active volcano Mount Erebus in Antarctica is discovered, and named by James Clark Ross. * January 28 – Ross discovers the "Victoria Barrier", later known as the Ross Ice Shelf. On the same voyage, he discovers the Ross Sea, Victoria Land and Mount Terror. * January 30 – A fire ruins and destroys two-thirds of the villa (modern-day city) of Mayagüez, Puerto Rico. * February 4 – First known reference to Groundhog Day in North America, in the diary of a James Morris. * February 10 – The Act of Union (''British North America Act'', 1840) is proclaimed in Canada. * February 11 – The two colonies of the Canadas are merged, into the United Province of Canada. * Febr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1908 Deaths
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album '' 63/19'' by Kool A.D. * '' Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album ''Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Echternach
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form " people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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